MathDB
Problems
Contests
National and Regional Contests
Serbia Contests
Serbia Team Selection Test
1987 Yugoslav Team Selection Test
Problem 2
Problem 2
Part of
1987 Yugoslav Team Selection Test
Problems
(1)
composition of function involving sqrt(2+sqrt(2))
Source: Yugoslav TST 1987 P2
5/28/2021
Let
f
(
x
)
=
2
+
2
x
+
2
−
2
−
2
−
2
x
+
2
+
2
f(x)=\frac{\sqrt{2+\sqrt2}x+\sqrt{2-\sqrt2}}{-\sqrt{2-\sqrt2}x+\sqrt{2+\sqrt2}}
f
(
x
)
=
−
2
−
2
x
+
2
+
2
2
+
2
x
+
2
−
2
. Find
f
(
f
(
⋯
f
⏟
1987
times
(
x
)
⋯
)
)
\underbrace{f(f(\cdots f}_{1987\text{ times}}(x)\cdots))
1987
times
f
(
f
(
⋯
f
(
x
)
⋯
))
.
function
algebra